Question

The supersonic aircraft Concorde has a length of 62.0 m when sitting on the ground on a typical day when the temperature is 18.0 ℃. The Concorde is primarily made of aluminum. In flight at twice the speed of sound, friction with the air warms the Concorde's skin and causes the aircraft to lengthen by29.0 cm. (The passenger cabin is on rollers, so the airplane expands around the passenger cabin.)

Take the coefficient of linear expansion for aluminum to be α = 2.40×10⁻⁵ ℃.

What is the temperature T of the Concorde's skin in flight?

Answer 1

Concepts and reason

The concept used to solve this problem is thermal expansion.

Initially, use the relation between change in length, original length, and linear expansion coefficient to calculate the change in temperature.

Then, finally use the change in temperature and the temperature on the ground to calculate the temperature of the Concorde’s skin in flight.

Fundamentals

Expression for the linear expansion is,

Here, is the change in length, is the linear expansion of coefficient, is the original length, and is the change in temperature.

Rearrange the above equation to get the change in temperature,

Expression for the change in temperature is,

Here, T is the temperature of the Concorde’s skin in flight and is the temperature on the ground.

Rearrange the above equation to get the temperature of the Concorde’s skin in flight,

Expression for the change in temperature,

Substitute for , for , and for .

Expression for the temperature of the Concorde’s skin in flight is,

Substitute for T and for .

Ans:

The temperature of the Concorde’s skin in flight is .